Re: Partial Differential Equation
- To: mathgroup at smc.vnet.net
- Subject: [mg26660] Re: Partial Differential Equation
- From: "Kevin J. McCann" <KevinMcCann at home.com>
- Date: Wed, 17 Jan 2001 00:47:16 -0500 (EST)
- References: <93r7gq$4q4@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Philippe,
The problem you have posed is a 2-point boundary value problem which Mathematica
often has difficulty with. The solution is to turn it into a one-point BVP,
and find the initial condition on T(0) that gives the desired T'(1). The
technique is often called a shooting technique.
I have sent you a NB separately that gives my attempt.
Cheers,
Kevin
The wise words of P. Poinas on 13 Jan 2001 22:47:38 -0500:
> Dear Group,
>
> I am trying to solve the following problem:
>
> \!\(\(\(NDSolve[{\(T''\)[R] + \((1/\((R + 0.05)\))\)\ \(T'\)[R] -
> 10\^\(-8\)\ \ T[R]\^4 == 0, \(T'\)[0] == \(-0.07\), \
> \(T'\)[1] ==
> 0}, \ T, \ {R, \ 0, \ 1}]\)\(\ \)\)\)
>
> and I get the following message:
>
> NDSolve::"inrhs": "Differential equation does not evaluate to a number
> or the \
> equation is not an nth order linear ordinary differential equation."
>
> I know that this error is because I am defining the derivative at 2
> different R values:
>
> at R=0, T'[0 ]= -0.07
> and R=1, T'[1] = 0
>
> hence it is not an initial boundary condition.
>
> 1) How can I turn around the problem?
>
>
> Actually, I found the Mathematica Book (V4) very weak on the subject. In
> page 924, it seems possible in In[7] to find a solution to a linear
> differential equation, even with 2 boundary conditions defined at 2
> different x values! My problem being not linear cannot therefore be
> solved. But Mathematica does not mentioned the linearity as a show
> stopper.
>
> 2) Does anybody know a better description of Mathematica's capacity?
>
> Thank you for helping me,
>
>
> Philippe Poinas
>
>